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Chapter 61: Practice Exercises
An astronauts uses a pendulum to determine the acceleration of gravity on a planet.
When a 0.05- kilogram mass is attached to a vertical spring, it is observed that it stretches 0.03 m.
There is a massless spring with a force constant of 50 N/m.
The system is on a horizontal surface.
There is a massless spring with a force constant of 20 N/m.
The system is on a surface with an amplitude of 4 cm.
A 2- kilo mass is attached to a spring.
10 J is the total energy of the system.
Two springs with force constants k 1 and k 2 are attached to a mass M. The mass can move over the surface.
There are two arrangements for the mass and springs.
A mass M is attached to two elastic strings made of the same material.
Equal tensions T exist in the two strings as shown below, because the mass is displaced vertically upward by a small displacement D y.
The mass starts to move up and down.
The tensions will not change if the displacement is small.
The pendula and springs can be used as timekeeping devices.
Compare the accuracy of these devices to the accuracy of timekeeping devices on the Moon, where gravity is 1/6 that of Earth's.
The values given in the question are 0.25 m.
We find that g is 17.5 m/s 2 using the values given in the question.
The period is given by the formula T=2pm/k.
We find that T is 0.35 s using the values given in the question.
E is the value given in the question.
We need to change the centimeters to meters to find a v of 0.28 m/s.
The total energy of the system will be affected if the spring and the amplitude of oscillations remain the same.
Newton's third law states that the forces must be equal and opposite.
There is a period of oscillation for arrangement.
The effective spring constant increases when the springs are connected in parallel.
The acceleration is proportional to the displacement and only for small angles is a pendulum a representation.
The object's mass can be determined using springs and horizontal oscillations, since the period of a horizontally oscillating mass on a spring is independent of the acceleration due to gravity.
The spring's period will be unaffected since the pendulum will have a longer period on the Moon.
The hanging mass-on-a-spring system will be stretched six times less on the Moon than it is on Earth.
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